Joseph Katuka's layup put the Colonials (15-11, 5-8 Atlantic 10 Conference) ahead 61-60 with 8:39 to go, their first lead since the 15:08 mark.
George Washington pushed the lead to as many as five, before the Explorers (11-16, 3-10) tied it with 4:43 remaining.
However, Kromah hit a free throw, Smith a dunk and Kromah followed with a layup to put the Colonials ahead for good, 72-67, with 3:24 left.
Katuka finished with 10 points and a career-high 14 rebounds for George Washington, which snapped a four-game losing streak to La Salle.
Rodney Green scored 21 points to lead La Salle, which lost its seventh straight.
The Explorers shot just 17.6 percent from 3-point range in the second half.